The fire broke out at around 5:26 pm in the Zuxintang Foot Massage Parlor in Tiantai County, state-run Xinhua news agency reported.
People were seen jumping out of the windows, eye witnesses said.
Eight people were found dead in the fire, while another 10 died in hospital after medical efforts failed, officials said.
Pictures on microblog Sina Weibo showed a building engulfed by heavy smoke and people jumping out of windows, while firefighters were trying to tame the blaze.
An investigation into the accident is under way, the report said.